Tips for Interpreting CAT output:CAT performs a statistical analysis on input data. A successful analysis, however, is dependent on the operator's knowledge of what constitutes valid data for this operation, and appropriate interpretation of the results obtained through the statistical program. There are many underlying assumptions for the data, if analyses are to be successful.

Major assumptions are stationarity, independence of data, homogeneity of variance and normally distributed noise. For data modeling by cosinor, goodness of fit of the model to the data is also an underlying assumption - you want to know how closely the model fits the data, in order to know if the result will be useful. While it is not always possible to satisfy all underlying assumptions, some data conditioning can bring data closer into alignment with the requirements of the analytical methods. Pre-processing, or conditioning, techniques include detrending, data transformations (log, square root...) and binning or averaging. CAT does not perform pre-processing except for binning. It is noted here that certain types of data, such as animal activity, or circulating hormone levels, are not normally distributed and have heterogeneous variance. Also noted, a slowly varying variable such as body temperature, if sampled too often, violates the assumption of independence.

The data used as input to Cat (but not CatCosinor) is assumed to be equidistant, and discrete (except for the luminance column). CAT assumes you are aware of these underlying assumptions. Smoothing and Actogram are helpful tools as you review data characteristics, and are used in conjunction with standard deviation of data, and other statististical measures.

Use Smoothing and Actogram to validate your data, checking for stationarity, as well as anomalies or extensively interpolated areas that can skew analysis. If gaps in data are too large, the interpolation performed by CAT may not be adequate, requiring manual intervention. Parameter MaxGap sets the maximum gap you wish to allow -- if gaps above size are found, that the program will stop with an error. This output has an example of a large gap that has been interpolated by CAT, with undesireable results: see Actogram between 4:01 and 7:21.

Analysis of periodicity is more successful when the input data series is several times as long as the period you are testing for. If the default lag of 1/3 is used for the AutoCorrelation function, it is important to have more than 3 periods represented in the input data.

Reading a Periodogram requires some experience. Of note: Not all spectral lines can be read as significant frequencies in the data. For example, two large spectral lines, adjacent to each other, likely represent one frequency in the data whose value falls between the frequency of those two lines. Note also: a Periodogram does not represent the significance of the spectral lines! Longer lines are more significant than shorter lines, but one is still not sure if any are significant. Another method is needed to find significance.

A Periodogram uses aFourier transform to break down finite-energy non-periodic waveforms into sinusoids. The Fourier series describes the decomposition of periodic waveforms, such that that any periodic waveform can be formed by the sum of a (possibly infinite) set of fundamental and harmonic components. In reading a Periodogram, it can be helpful to understand how some common waveforms might appear when analyzed by periodogram:

Common periodic waveforms (t is time):

Sine wave: sin (2 π t). A perfect sine will be represented by a single peak in the periodgram -- BUT only if it falls exactly on one of the frequencies represented by the periodogram. If it falls between lines, it may be represented by multiple lines..

Square wave: saw(t) − saw (t − duty). A square wave of constant period will be seen as a periodogram with spectral lines at odd harmonics that fall off at −6 dB/octave.

Sawtooth wave: 2 (t − floor(t)) − 1. This looks like the teeth of a saw. It is used as the starting point for subtractive synthesis, as a sawtooth wave of constant period contains odd and even harmonics that fall off at −6 dB/octave.

The above waveforms are all periodic, so one might expect to see a single line on the Periodogram indicating the period, but that is not the case. Non-sinusoidal waveforms are composed of multiple waveforms of different frequencies. For this reason, even a periodic waveform may appear as multiple frequency lines on a periodogram. See Analysis of Rhythms using R: Chronomics Analysis Toolkit (CAT) for further details on using CATkit.